EP1354248B1 - Procede pour la simulation de systemes mecatroniques - Google Patents

Procede pour la simulation de systemes mecatroniques Download PDF

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Publication number
EP1354248B1
EP1354248B1 EP01990371A EP01990371A EP1354248B1 EP 1354248 B1 EP1354248 B1 EP 1354248B1 EP 01990371 A EP01990371 A EP 01990371A EP 01990371 A EP01990371 A EP 01990371A EP 1354248 B1 EP1354248 B1 EP 1354248B1
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EP
European Patent Office
Prior art keywords
simulating
time
modal
forces
matrix
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German (de)
English (en)
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EP1354248A1 (fr
Inventor
Carsten Hamm
Michael Louis
Wolfgang Papiernik
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Siemens AG
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Siemens AG
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Priority claimed from DE10137909A external-priority patent/DE10137909A1/de
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    • G—PHYSICS
    • G05—CONTROLLING; REGULATING
    • G05B—CONTROL OR REGULATING SYSTEMS IN GENERAL; FUNCTIONAL ELEMENTS OF SUCH SYSTEMS; MONITORING OR TESTING ARRANGEMENTS FOR SUCH SYSTEMS OR ELEMENTS
    • G05B17/00—Systems involving the use of models or simulators of said systems
    • G05B17/02—Systems involving the use of models or simulators of said systems electric

Definitions

  • the invention relates to a method for simulating mechatronic systems.
  • Such mechatronic systems have at least one mechanical and electrotechnical / electronic component, which combine in terms of construction, structure and function to form a single system. This fact is expressed by the term "mechatronic".
  • M is the mass matrix
  • D the damping matrix
  • C is the stiffness matrix
  • F ⁇ the nodal forces
  • u the node displacement vector
  • t the time.
  • This calculation rule is integrated into such a finite element model in a manner known to those skilled in the art.
  • Object of the present invention is therefore to provide a method of the type mentioned, which provides a higher simulation accuracy with respect to the previously described, known methods lower computational complexity.
  • the transformation of the fundamental equation of motion to linear differential equations of the first order takes place in the modal space. This ensures that predefinable eigenmodes can be selected or deselected before time discretization takes place.
  • actuators with any transfer function can be used.
  • the fundamental equation of motion (1) described at the outset is initially transformed according to the invention to ordinary standard equation of state, in particular to first order linear differential equations, preferably in modal space. These are then time-discretized so that only algebraic difference equations need to be solved to determine the time behavior of the system instead of the differential equations, which is easier and more effectively possible with today's computer systems.
  • the time grid that is to say the calculation of the difference equations, is only to be updated in the sampling grid of the control processor. This is the case because only the values in the computer clock of a computer executing the calculation are of importance.
  • the calculation step size can be reduced from typically 1 ... 5 msec to 100 ⁇ sec, depending on the required accuracy.
  • the time saving factor over the known methods outlined above is more than 1000.
  • modal coordinates and their time derivatives are suitably used. Given a coordinate transformation of a finite element system given in the form of the fundamental equation of motion (1) with the matrix of eigenvectors X and the generalized modal coordinates q ⁇ before, the system can be transformed into the so-called "modal space”.
  • M ⁇ X ' ⁇ M ⁇ X the modal mass matrix
  • D ⁇ X ' ⁇ D ⁇ X the modal damping matrix
  • X is the matrix of the eigenvectors of the undamped system
  • q ⁇ the generalized modal coordinates
  • u ⁇ X ⁇ q ⁇ the nodal shifts
  • Q ⁇ X ' ⁇ F ⁇ the generalized modal forces.
  • the description of the state in the modal space also has the advantage that specific, specifiable eigenmodes (de) can be selected before the time discretization takes place.
  • FIG. 1 shows a finite element model of a simple mechanical bridge B on which a carriage S can be moved in the x-direction x.
  • a sketched coordinate system shows the spatial orientation in x-direction x, y-direction y and z-direction z.
  • exemplary connection nodes 1 to 4 a measuring node 5 and a force introduction node 6 are shown, which serve for the simulation.
  • the stiffness at the connection nodes is therefore equal to 0 in the x-direction x, while in the y- and z-direction y, z is predetermined by the rigidity of the guides. Volume elements are used to represent the structural behavior.
  • the system order after the discretization according to the calculation rules (7) and (8) is also of order 43.
  • the simulation duration of a step response according to the method according to the invention is, for example, 130 msec with the program 'Matlab / Simulink / Realtime Workshop'.
  • the simulation of the same process in a conventional manner takes, with exemplary use of the software instrument PERMAS '11 min., I. the simulation time can be shortened by the factor 5000 by application of the present patent application.

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  • Physics & Mathematics (AREA)
  • General Physics & Mathematics (AREA)
  • Engineering & Computer Science (AREA)
  • Automation & Control Theory (AREA)
  • Management, Administration, Business Operations System, And Electronic Commerce (AREA)
  • Complex Calculations (AREA)
  • Feedback Control In General (AREA)

Claims (6)

  1. Procédé de simulation d'un système mécatronique, le système mécatronique comportant au moins un composant mécanique et électrotechnique/électronique, à partir d'une équation de mouvement de base. M ⋅ u → ¨ ( t ) + D ⋅ u → ˙ ( t ) + C ⋅ u → ( t ) = F ( t )
    Figure imgb0058
     pour modéliser le système, où
    M désigne la matrice d'inertie,
    D désigne la matrice d'amortissement
    C désigne la matrice de raideur,
    F →
    Figure imgb0059
     désigne les forces aux points nodaux,
    u →
    Figure imgb0060
     désigne et le vecteur de translation nodale et
    t désigne le temps
    caractérisé par les étapes opératoires suivantes :
    - transformation de l'équation de mouvement de base en des équations différentielles linéaires de premier ordre,
    - autre transformation des équations différentielles linéaires en des équations d'état à valeurs discrètes dans le temps,
    - détermination du comportement dans le temps du système par actualisation des équations différentielles algébriques résultantes dans la trame d'analyse d'un processeur de régulation associé.
  2. Procédé de simulation d'un système mécatronique selon la revendication 1, caractérisé en ce que la transformation de l'équation de mouvement de base en équations différentielles linéaires de premier ordre est effectuée dans l'espace modal.
  3. Procédé de simulation d'un système mécatronique selon la revendication 1 ou 2, caractérisé en ce que, pour simuler des retards des forces aux points nodaux, des équations différentielles correspondantes sont ajoutées et prises en compte dans la détermination du comportement dans le temps du système.
  4. Procédé de simulation d'un système mécatronique selon la revendication 3, caractérisé en ce que, dans le système, des forces non retardées supplémentaires ( F → D )
    Figure imgb0061
     sont prises en compte dans la détermination du comportement dans le temps du système en scindant le vecteur force ( F → )
    Figure imgb0062
     en une partie forces retardées ( F → R )
    Figure imgb0063
     et une partie forces non retardées ( F → D ) .
    Figure imgb0064
  5. Procédé de simulation d'un système mécatronique selon la revendication 3 ou 4, caractérisé en ce que les équations différentielles destinées à la simulation de retards des forces aux points nodaux ( F → )
    Figure imgb0065
     sont décrites avec un élément de régulation PT1 comme actionneur, la force de consigne ( F → W )
    Figure imgb0066
     représentant la grandeur de commande de ce régulateur.
  6. Procédé de simulation d'un système mécatronique selon l'une des revendications précédentes 2 à 5, caractérisé en ce que des coordonnées modales et leurs dérivations par rapport au temps servent à décrire la partie mécanique du système mécatronique, lesquelles coordonnées et dérivations permettant d'obtenir l'équation de mouvement de base M ‾ ⋅ q → ¨ ( t ) + D ‾ ⋅ q → ˙ ( t ) + C ‾ ⋅ q → ( t ) = Q ‾ ( t )
    Figure imgb0067
     où
    M̅ = X'·M·X désigne la matrice d'inertie modale
    D̅ = X'·D·X désigne la matrice d'amortissement modale
    C̅ = X'·C·X désigne la matrice de raideur modale
    X désigne la matrice des vecteurs propres du système non amorti,
    q →
    Figure imgb0068
     désigne les coordonnées modales généralisées,
    u → = X ⋅ q →
    Figure imgb0069
     désigne les translations de point modal
    Q → = X ′ ⋅ F →
    Figure imgb0070
     désigne les forces modales généralisées.
EP01990371A 2001-01-18 2001-12-21 Procede pour la simulation de systemes mecatroniques Expired - Lifetime EP1354248B1 (fr)

Applications Claiming Priority (5)

Application Number Priority Date Filing Date Title
DE10102313 2001-01-18
DE10102313 2001-01-18
DE10137909 2001-08-02
DE10137909A DE10137909A1 (de) 2001-01-18 2001-08-02 Verfahren zur Simulation mechatronischer Systeme
PCT/DE2001/004890 WO2002057857A1 (fr) 2001-01-18 2001-12-21 Procede pour la simulation de systemes mecatroniques

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EP1354248A1 EP1354248A1 (fr) 2003-10-22
EP1354248B1 true EP1354248B1 (fr) 2006-06-21

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US (1) US7236913B2 (fr)
EP (1) EP1354248B1 (fr)
JP (1) JP4612989B2 (fr)
DE (1) DE50110293D1 (fr)
WO (1) WO2002057857A1 (fr)

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* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
FR2934393B1 (fr) * 2008-07-25 2010-09-10 Commissariat Energie Atomique Procede de realisation d'un systeme mecatronique flexible
US8255197B2 (en) * 2008-09-30 2012-08-28 Rockwell Automation Technologies, Inc. Simulation of tuning effects for a servo driven mechatronic system
EP2988181B1 (fr) 2014-08-19 2019-07-03 Siemens Aktiengesellschaft Dispositif de réglage à compensation d'erreur adaptative
EP3115857A1 (fr) 2015-07-09 2017-01-11 Siemens Aktiengesellschaft Procédé de détermination de trajectoire pour mouvements de temps mort
EP3131202A1 (fr) 2015-08-11 2017-02-15 Siemens Aktiengesellschaft Procede d'inversion de filtre pour une commande de machine
EP3136192A1 (fr) 2015-08-24 2017-03-01 Siemens Aktiengesellschaft Procede de commande de mouvement d'un outil et dispositif de commande
EP3144754A1 (fr) 2015-09-17 2017-03-22 Siemens Aktiengesellschaft Amortissement des oscillations de charge sans moyen de mesure supplementaire cote charge
CN111395173B (zh) * 2020-03-23 2021-06-29 东南大学 一种基于bim的钢桁拱桥螺栓连接施工精度控制方法
CN115438513B (zh) * 2022-11-07 2023-03-31 人工智能与数字经济广东省实验室(广州) 分数阶阻尼减震结构抗震设计的分析方法、系统、设备和介质

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US4881172A (en) 1986-12-22 1989-11-14 Lord Corporation Observer control means for suspension systems or the like
US4984173A (en) * 1989-06-09 1991-01-08 General Electric Company System for aligning a rotating line-shaft
JP2730195B2 (ja) * 1989-06-30 1998-03-25 三菱電機株式会社 結合振動特性解析装置
JPH03100801A (ja) * 1989-09-14 1991-04-25 Toshiba Corp 制御装置
US5422834A (en) * 1991-07-02 1995-06-06 Hitachi, Ltd. Simulation method and system for simulating drive mechanism
DE4207541B4 (de) * 1992-03-10 2006-04-20 Robert Bosch Gmbh System zur Steuerung einer Brennkraftmaschine
US5590261A (en) * 1993-05-07 1996-12-31 Massachusetts Institute Of Technology Finite-element method for image alignment and morphing
US6427127B1 (en) * 1998-07-16 2002-07-30 Micro Motion, Inc. Vibrating conduit process parameter sensors, operating methods and computer program products utilizing complex modal estimation

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US20040049368A1 (en) 2004-03-11
JP2004523824A (ja) 2004-08-05
JP4612989B2 (ja) 2011-01-12
WO2002057857A1 (fr) 2002-07-25
DE50110293D1 (de) 2006-08-03
US7236913B2 (en) 2007-06-26
EP1354248A1 (fr) 2003-10-22

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